M.Ing (Electrical and Electronic Science) / High frequency magnetic components have significant advantages related to cost and physical size compared to their low frequency counterparts. The advent of high frequency power switch technology made the transformer frequency a variable and recent advances in this field have been ever pushing the switching frequency of higher power converters. Although high frequency inductors and transformers have been used and applied extensively to an increasingly broad range of applications over recent decades, analysis and design of these devices involves certain difficulties, related to extra losses due to eddy currents as well as smaller cooling surfaces, to the developer and designer. Numerical simulations of eddy currents in windings are slow, if not impossible in many cases, due to the large mesh impositions required in order to converge. Eddy currents and thermal constraints impose limitations on flux- and current densities, complicating the design. As yet, a convenient means of design, analysis and optimization of the physical magnetic topology does not exist. In this study, a method for analysing eddy currents in windings, usmg a combined analytical and numerical approach, is presented and implemented in a CAD tool. The one dimensional solutions for eddy currents in strip conductors are written in a more flexible form. A new approach to magnetic component design, called scant modelling, is presented and applied to two practical examples. The scant model comprises a minimum number of functional and form parameters in analysing and optimizing a design, but considers eddy current effects, thermal constraints and the effects of physical size and shape of core and windings at high frequencies.

A comprehensive and general analysis of the electromagnetic fields, power dissipation, and energy storage within transformer windings is presented. Emphasis is placed on applications in switched-mode power conversion. One-dimensional radial variation of the field quantities is assumed. The first phase of the investigation is for sinusoidal excitation; solutions for the current density and magnetic field intensity are derived and studied in order to develop a fundamental understanding of the basic phenomena. Expressions for the power dissipation and energy storage in both single- and multi-layer windings are then derived which, upon investigation, yield a technique for minimizing the power dissipation by choosing an optimum conductor thickness. Several levels of accuracy, ranging from exact solutions to very simple and physically meaningful series approximations, are defined and examined to determine their usefulness and range of validity. The time-harmonic treatment is generalized to arbitrary periodic exoitation by means of Fourier analysis, resulting in a powerful extension of its applicability to any possible converter topology. Results for several representative waveshapes are presented from which a fundamental dependence cn the waveform bandwidth is discovered. Practical application of the theoretical analysis is considered by developing models for several couon winding types: single and multi-filar round wire, litz wire, and sheet conductors. Experimental results are presented and compared with the theoretical results for each of these cases. Finally, a design procedure is outlined for switched—mode pour transformers which is based on this work. / Ph. D.

Frequency response analysis (FRA) of transformers is universally accepted as a highly sensitive tool to detect deformations in its windings. This is evident from the fact that customized commercial equipment (popularly called FRA or SFRA instruments) are used and recently the IEEE has issued a draft trial-use guide. Nevertheless, use of FRA is still limited to only detection and there is little progress towards its use for localization of winding deformation. Toward this end, a possible approach would be to compare the healthy and deformed systems in a suitable domain, e.g., their respective models could be compared. In this context, the mutually-coupled ladder network is ideally suited because not only does it map the length of the winding to sections of the ladder network, but, also inherently captures all subtle intricacies of winding behaviour under lightning impulse excitations insofar as the terminal response, internal oscillations and voltage distributions are concerned. The task of constructing a ladder network from frequency response is not trivial, and so exploration of newer methods is imperative. A system can comprehensively be characterized by its frequency response. With this as the starting point, many approaches exist to construct the corresponding rational function (in s-domain). But, the subsequent step of converting this rational function into a physically-realizable mutually-coupled ladder network has, as yet, remained elusive. A critical analysis of the circuit synthesis literature reveals that there exists no analytical procedure to achieve this task, a fact unequivocally stated by Guillemin in his seminal book "Synthesis of Passive Networks". In recent years, use of iterative methods to synthesize such ladder networks has also been attempted with some degree of success. However, there exists a lot of scope for improvement. Based on this summary, the objectives of this thesis are as follows- _ Development of an analytical procedure, if possible, to synthesize a mutually-coupled ladder network starting from the s-domain representation of the frequency response _ Construction of a nearly-unique, mutually-coupled ladder network employing constrained optimization technique and using frequency response as input, with time-efficiency, physical realizability and repeatability as its features In Chapter 2, analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically-realizable ladder network with inductive couplings (between any two sections) and losses considered. The number of sections in the ladder network can vary, but, its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalized expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple, and guarantees a unique network. Presently, the formulation can synthesize a unique ladder network up to 6-sections. Although it is an analytical solution, there are issues which prevent its implementation with actual FRA data. Keeping the above aspect in mind, the second part of the thesis presents results of employing an artificial bee colony search algorithm for synthesizing a mutuallycoupled lumped-parameter ladder network representation of a transformer winding, starting from its measured magnitude frequency response. The bee colony algorithm is modified by defining constraints and bounds to restrict the search-space and thus ensure synthesis of a nearly-unique ladder network, corresponding to each frequency response. Ensuring near-uniqueness while constructing the reference circuit (i.e., a uniform healthy winding) is the objective. The proposed method is easy to implement, time-efficient, ensures physical realizability and problem associated with supply of initial guess in existing methods is circumvented. Experiments were performed on two types of actual, single, isolated transformer windings (continuous-disc and interleaveddisc) and the results are encouraging. Further details are presented in the thesis.

Thesis (MScEng)-- Stellenbosch University, 2013. / ENGLISH ABSTRACT: The objective of this project is to develop an electromagnetic model that can be used to accurately calculate the voltage distribution in a transformer winding structure when excited with standard impulse excitation waves. This voltage distribution is required during the design stage of a power transformer to ensure that the insulation is capable of withstanding the occurring electric field stresses during these tests. This study focuses on the modelling of a single disk-type power transformer winding without the presence of an iron-core. Methods of calculating self- and mutual-inductances of transformer windings are presented and validated by means of finite element method software simulations. The same is done for the calculation methods used for calculating the capacitances in and around the winding structure. The calculated and FEM-simulated results are compared to measured values as a final stage of validation. The methods used to calculate the various model parameters seem to produce results that agrees well with measured values. The non-linear frequency dependant dissipative nature of transformer windings is also investigated and a methodology to take this into account is proposed and implemented. The complete modelling methodology proposed in this thesis, which includes the calculation of the model parameters, model synthesis and solver algorithm, are applied to an actual case study. The case study is performed on an air-core reactor manufactured using a disk-type power transformer winding. The reactor is excited with standard lightning impulse waves and the voltages along the winding are measured. The calculated and measured voltage wave forms are compared in both the frequency and time-domain. From the comparison it is found that the model accurately represents the actual transient voltage response of the testunit for the frequency range of interest during standard factory acceptance tests. / AFRIKAANSE OPSOMMING: Die doel van hierdie projek is om 'n elektromagnetiese model te ontwikkel wat gebruik kan word om die spanningsverspreiding in 'n transformatorwindingstruktuur te bereken as standaard weerligimpulstoetse toegedien word. Hierdie spanningsverspreiding word vereis tydens die ontwerpstadium van ‘n kragtransformator om te verseker dat die isolasie in staat is om die elektriese veldsterkte tydens hierdie toetse te weerstaan. Hierdie studie fokus op die modelering van 'n enkele skyftipe-kragtransformatorwinding sonder die teenwoordigheid van 'n ysterkern. Metodes van berekening van self- n wedersydse-induktansie van transformatorwindings word aangebied en getoets deur middel van Eindige-Element-Metode (EEM) simulasies. Dieselfde word gedoen vir die metodes wat gebruik word vir die berekening van die kapasitansies in en rondom die windingstruktuur. Die berekende en EEM-gesimuleerde resultate word vergelyk met die gemeete waardes as 'n finale vlak van bekragtiging. Die metodes wat gebruik word om die verskillende modelparameters te bereken vergelyk goed met gemete waardes. Die nie-lineêre frekwensie-afhanklike verliese van transformatorwindings word ook ondersoek en 'n metode om hierdie in ag te neem is voorgestel en geïmplementeer. Die volledige voorgestelde modeleringsmetodiek in hierdie tesis, wat die berekening van die modelparameters, modelsintese en oplosingsalgoritme insluit word toegepas op 'n werklike gevallestudie. Die gevallestudie is uitgevoer op 'n lugkern-reaktor wat 'n skyftipe-kragtransformatorwinding. Die reaktor word onderwerp aan die standaard weerligimpuls golwe en die spanning al langs die winding word gemeet. Die berekende en gemete spanning golf vorms word met mekaar vergelyk in beide die frekwensie- en tyd-vlak. Uit die vergelyking blyk dit dat die model die werklike oorgangspanningsweergawe van die toetseenheid akkuraat verteenwoordig vir die frekwensie reeks van belang tydens standaard fabriekaanvaardingstoetse.